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y=ctg(2e^x)-(x*arccos3x)/(3-lnx)
Derivada de la función/ y=ctg(2e^x)-(x*arccos3x)/(3-lnx)

Derivada de y=ctg(2e^x)-(x*arccos3x)/(3-lnx)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   /   x\   x*acos(3*x)
cot\2*E / - -----------
             3 - log(x)
−xacos⁡(3x)3−log⁡(x)+cot⁡(2ex)- \frac{x \operatorname{acos}{\left(3 x \right)}}{3 - \log{\left(x \right)}} + \cot{\left(2 e^{x} \right)} 
cot(2*E^x) - x*acos(3*x)/(3 - log(x))
Gráfica
02468-8-6-4-2-1010-10000000001000000000
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Primera derivada [src] 
                  3*x                                              
-acos(3*x) + -------------                                         
                __________                                         
               /        2                                          
             \/  1 - 9*x       acos(3*x)       /        2/   x\\  x
-------------------------- - ------------- + 2*\-1 - cot \2*E //*e 
        3 - log(x)                       2                         
                             (3 - log(x))
2(−cot⁡2(2ex)−1)ex+3x1−9x2−acos⁡(3x)3−log⁡(x)−acos⁡(3x)(3−log⁡(x))22 \left(- \cot^{2}{\left(2 e^{x} \right)} - 1\right) e^{x} + \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{3 - \log{\left(x \right)}} - \frac{\operatorname{acos}{\left(3 x \right)}}{\left(3 - \log{\left(x \right)}\right)^{2}}
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Segunda derivada [src] 
                                                                           3*x                /         2  \                                                            
                                                         -acos(3*x) + -------------           |      9*x   |                                                            
                                                                         __________         3*|2 + --------|                                                            
                                                                        /        2            |           2|                                                            
    /       2/   x\\  x                3                              \/  1 - 9*x             \    1 - 9*x /          2*acos(3*x)        /       2/   x\\    /   x\  2*x
- 2*\1 + cot \2*e //*e  + ---------------------------- + -------------------------- - --------------------------- + ---------------- + 8*\1 + cot \2*e //*cot\2*e /*e   
                             __________                                      2           __________                                3                                    
                            /        2               2        x*(-3 + log(x))           /        2                  x*(-3 + log(x))                                     
                          \/  1 - 9*x  *(-3 + log(x))                                 \/  1 - 9*x  *(-3 + log(x))
8(cot⁡2(2ex)+1)e2xcot⁡(2ex)−2(cot⁡2(2ex)+1)ex−3(9x21−9x2+2)1−9x2(log⁡(x)−3)+31−9x2(log⁡(x)−3)2+3x1−9x2−acos⁡(3x)x(log⁡(x)−3)2+2acos⁡(3x)x(log⁡(x)−3)38 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right) e^{2 x} \cot{\left(2 e^{x} \right)} - 2 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right) e^{x} - \frac{3 \left(\frac{9 x^{2}}{1 - 9 x^{2}} + 2\right)}{\sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)} + \frac{3}{\sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{2}} + \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{x \left(\log{\left(x \right)} - 3\right)^{2}} + \frac{2 \operatorname{acos}{\left(3 x \right)}}{x \left(\log{\left(x \right)} - 3\right)^{3}}
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Tercera derivada [src] 
                                                                        3*x                                                                                                     /                  3*x     \                                                                                                    /         2  \                /         2  \       
                                                      -acos(3*x) + -------------                                                                                              2*|-acos(3*x) + -------------|                                                                                                    |     27*x   |                |      9*x   |       
                                                                      __________                                                                                                |                __________|                                                                                               27*x*|4 + --------|              6*|2 + --------|       
                     2                                               /        2                                                                                                 |               /        2 |                                                                                                    |           2|                |           2|       
     /       2/   x\\   3*x     /       2/   x\\  x                \/  1 - 9*x           2/   x\ /       2/   x\\  3*x                 12                    6*acos(3*x)        \             \/  1 - 9*x  /      2*acos(3*x)         /       2/   x\\    /   x\  2*x               27*x                        \    1 - 9*x /                \    1 - 9*x /       
- 16*\1 + cot \2*e // *e    - 2*\1 + cot \2*e //*e  - -------------------------- - 32*cot \2*e /*\1 + cot \2*e //*e    - ------------------------------ - ----------------- - ------------------------------ - ----------------- + 24*\1 + cot \2*e //*cot\2*e /*e    + ---------------------------- - --------------------------- + ------------------------------
                                                           2              2                                                   __________                   2              4          2              3           2              3                                                  3/2                            3/2                      __________               
                                                          x *(-3 + log(x))                                                   /        2               3   x *(-3 + log(x))          x *(-3 + log(x))           x *(-3 + log(x))                                         /       2\                 2   /       2\                        /        2               2
                                                                                                                         x*\/  1 - 9*x  *(-3 + log(x))                                                                                                                  \1 - 9*x /   *(-3 + log(x))    \1 - 9*x /   *(-3 + log(x))   x*\/  1 - 9*x  *(-3 + log(x))
−27x(27x21−9x2+4)(1−9x2)32(log⁡(x)−3)+27x(1−9x2)32(log⁡(x)−3)2−16(cot⁡2(2ex)+1)2e3x−32(cot⁡2(2ex)+1)e3xcot⁡2(2ex)+24(cot⁡2(2ex)+1)e2xcot⁡(2ex)−2(cot⁡2(2ex)+1)ex+6(9x21−9x2+2)x1−9x2(log⁡(x)−3)2−12x1−9x2(log⁡(x)−3)3−3x1−9x2−acos⁡(3x)x2(log⁡(x)−3)2−2(3x1−9x2−acos⁡(3x))x2(log⁡(x)−3)3−2acos⁡(3x)x2(log⁡(x)−3)3−6acos⁡(3x)x2(log⁡(x)−3)4- \frac{27 x \left(\frac{27 x^{2}}{1 - 9 x^{2}} + 4\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(\log{\left(x \right)} - 3\right)} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(\log{\left(x \right)} - 3\right)^{2}} - 16 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right)^{2} e^{3 x} - 32 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right) e^{3 x} \cot^{2}{\left(2 e^{x} \right)} + 24 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right) e^{2 x} \cot{\left(2 e^{x} \right)} - 2 \left(\cot^{2}{\left(2 e^{x} \right)} + 1\right) e^{x} + \frac{6 \left(\frac{9 x^{2}}{1 - 9 x^{2}} + 2\right)}{x \sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{2}} - \frac{12}{x \sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{2}} - \frac{2 \left(\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}\right)}{x^{2} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{2 \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{6 \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{4}}
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Gráfico
Derivada de y=ctg(2e^x)-(x*arccos3x)/(3-lnx)
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